Electron Population Dynamics in Optically Pumped Asymmetric Coupled Ge/SiGe Quantum Wells: Experiments and Models

n-type doped Ge quantum wells with SiGe barriers represent a promising heterostructure system for the development of radiation emitters in the terahertz range such as electrically pumped quantum cascade lasers and optically pumped quantum fountain lasers. The non-polar lattice of Ge and SiGe provides electron-phonon scattering rates that are one order of magnitude lower than polar GaAs. We have developed a self-consistent numerical energy-balance model based on a rate equation approach which includes inelastic and elastic inter- and intra-subband scattering events and takes into account a realistic 2DEG distribution in all the subband states of the Ge/SiGe quantum wells by considering subband-dependent electronic temperatures and chemical potentials. This full-subband model is here compared to the standard discrete-energy-level model, in which the material parameters are limited to few input values (scattering rates and radiative cross-sections). To provide an experimental case study, we have epitaxially grown samples consisting of two asymmetric coupled quantum wells forming a three-level system, which we optically pump with a free electron laser. The benchmark quantity selected for model testing purposes is the saturation intensity at the 1-3 intersubband transition. The numerical quantum model prediction is in reasonable agreement with the experiments and therefore outperforms the discrete-energy-level analytical model, whose prediction of the saturation intensity is off by a factor 3.